Actually, "My World..." would probably have been renewed for at least one more season, had it not been for Red Skelton! CBS had unexpectedly canceled the veteran comedian's long-running series, and NBC moved quickly to sign him up (much as they had done with Jack Benny a few years earlier.) NBC could offer Skelton only a half-hour series, unlike the hour he'd had on CBS, and they canceled "My World..." pretty much to make room for him. Unfortunately, Skelton's NBC series was far below the quality of his CBS shows, and was dropped after one season. (The NBC shows were the basis of a Skelton video package offered a few years ago, they are practically unwatchable.)
http://www.tv.com/shows/my-world-and-welcome-to-it/